The 60Co Calibration of the ZEUS Calorimeters by Ling-Wai Hung Department of Physics, McGili University Montréal, Québec July 1991 A Thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillnlent of the requirements for the degree of 11aster of Science @ Ling-Wai Hung, 1991
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The 60Co Calibration of the ZEUS Calorimeters
by
Ling-Wai Hung Department of Physics, McGili University
Montréal, Québec July 1991
A Thesis submitted to the Faculty of Graduate Studies and Research
in partial fulfillnlent of the requirements for the degree of 11aster of Science
@ Ling-Wai Hung, 1991
( ...
Abstract
The calibration and quality control measurements of the ZEUS forward and rear calorimcters made using movable 60Co sources are described. The types of assembly faults discovcred from the l'uns taken first at CERN and then later at DESY from mid 1990 ta carly 1991 are prcsented. The VILS attenuation length as weIl as changes in the attC'lluation length of the scintillators can be monitored by the cobalt scans.
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Résumé
Le processus de calibration et de mise au point des calorinlC'trcs avant ct arriht> du détecteur ZEUS en utilisant ulle source mobile de 6OCO est d('C1it en lktail. L('s différentes erreurs d'assemblage découvertes lors des (,Xpl-I iell(,(~s rtH CEHN pHI!> à DESY au cours des années 1990 et 1991 sont égal{,!llent présl·ntées. L'clttéllll.\tion d('s dephaseurs et les changerneI1ts de la longueur d'atténuation d('~ ~cilltilli\klll" peu\'('lIt
être estimés en utilisant une source de 60Co.
iii
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Contents
Abstract ii
Résumé Hi
List of Figures vi
List of Tables ... Vill
Acknowledgements ix
1 Introduction 1 1.1 Background 1 1.2 Kinematics 3 1.3 HERA Physics 6 1.4 The ZEUS Detector 8
6 Conclusions and Outlook 84 6.1 Scanning in the ZEUS Hall . 84 6.2 Conclusions ......... 85
References 88
...
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List of Figures
1.1 Layout of the HERA Rmg . . . . . . . . . . . . . . . . . . . . . . .. 3 1.2 Feynman dwgrams of lowest order a) Ne and b) CC interactIOns .. 4 1.3 Polar dwgram (lf the kinematics for the final lepton (upprr parI) and the
CUITent Jet (lower part) ll'lth Imes of constant :r and Q2. Connectmg a gwen (:r, Q2) PO/lit wlth the 01'lgzn gives the laboratory momentum vutors, as shown by the e:ramplc for x = 0.5, Q2 = 5000Ce V 2. 7
1.4 Vicw of the ZHUS DetectaI' ... . . . . . . 9 1.5 Cross SectlOnal VICW of the ZEUS Detcclor. . . . . . . . . . . 10
2.1 FractlOnal Encrgy Loss for Electrons and PosItrons in Lead (j7-om Rev. of Pari. P1'Op., Phys Lei. B. Vol 239) . . . . . . . . . . . . . . . . .. 17
2.2 Pltoton C7'oss-sectlOn ln 1/ ad as a functlOn of photon cnergy. (from Rev. of Pari. Prop. 1980 ((fillOn) . . . . . . . . . . . . . . . . . . . . . .. 17
2.3 Average deposlted entrgy vs dcpth for electromagnetic showcrs of en-ergies 1. 20 and 75 Ge V . . . 19
2.4 Posttioning of FeAL modules 28 2 . .5 Posttioning of ReAL modules 28 2.6 View of a Large FeAL Module. 30 2.7 Thlckness D,stribution of FCAL seintillators . 31 2.8 Tyvek Paper Pattern used for FCA L EMC Seintlilators 32 2.9 View of WLS reading out scintillator . . . . . . . . . . 33
3.1 Absorptwn and Emission Spectra of SCSN, Y-1, and PM cathode 49 3.2 View of Ihe Source GUlde Tubes and Light Guides 50 3.3 Skelch of the outside driver scanning a module. 51 3.4 Source wire used in inside scannmg . . 52 3.5 Source wtre used zn outslde scanning 52 3.6 Layout of Elements in the Run Control 53 3.7 View of Source D/'wer from above 54 3.8 Vlew of Sour'cc Drwcr from the side 54
4.1 Layer' Structure used in Monte Carlo Simulation. Dislallrf'(I are in mm. 58 4.2 Monte Carlo of the Response function, R(z), of a Singl, '"', lIt/lllator,
before and after smoothmg . . . . . . 59 4.3 Real Response of a Single Scintillalor 59
VI
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LIST OF FIGURES VII
·1.4 lOTleoluled Response Function Repre~(nll1!g SlgTlal F/'om /lAC. Cll ·1..5 .\fol/te Codo flAC sectlOll Il,/th OIH' sem/tllalor 50f//> ... hlldoll'u! 61 4.6 .llonte Carlo of HAC Sfrl/Oll Il l ltl! dll1Jwgcd HL<; l'hf ji/'8/ .3:1 IOyf l'.'
haue a rcdlldlOn III lzghl output of :!09é fo/' thf jll',.,1 layf /', dl('1"u],'II1!1
111IW1'ly to 0% fol' tlu tIN nly·jirst la y(/', , t;2 -\.7 ,\fonte Carlo of /JAC sfcllOlI 1L,/th !!() layers jJlL • .,1!U{1II by (,')llll ()',!
4.8 Manie Car/a of /lAC ser/101l u'dh 20 layfrs Pll,-lud ouf (, 111111 {\:3 4.9 X- y dlstrzbutlOn of entrgy dfpOSlffd ln sfllltlllator ll'dh the .""Ol/J'('l ]l0-
siflOncd at 8 mm awoy, as !Il oufsll!c :,calll11llg. (l·t
5.1 Raw slgna/ from PAls n:adzng out bath s1de8 of Il 114(' ... ('cito1l G6 5.2 SIgnais from PAIs rtadmg Ollt both suies of a n0/'11Iai /lAC scellOn 67 .5.3 Signais fl'o»1 P.'rls rmdwg ouf bolh sliles of a normal HM(' ~I('IIOII III
FeAL 67 5..1 Signais from P'\[s rcadmg out both sides of a normal Il..1 co ~tcflOlI 111
FeAL . . 68 5.5 SIgnaIs fl'om PAIs reading out both s!df.S of a normal FU(' ln ue'AL. G8 5.6 Scans of Module CDN2, Tou'cr 14 llAC2 u'dh the l/I,.,u!r and oul ... u{c
methods 69 .5.i n'ldth of HACt SfctlOTlS from inslIlc and ouls/dr 8('(11/11/119 70 .5.S Bad sfacking . 72 ,5.9 S}lifhd Scwlzllmor ï:3 5.10 lncrrased Rfsponse from Shlflcd Scwllllaior ln NL14 7·1 5.11 Sli/fied EMC WLS. Nole the shal'p drop where the fir!'t sCIIl/Illa/or [(Jillr
should be md/catl1lg fhat the first layer lB not seen 76 5.12 Sttcking back 1'efiector. 77 5.13 Shadowed Scwttllator . 78 5.14 Bad homogenClty .. 80 5.15 Dl~tnbutlOn of the quantlty e-d/ À ln FeAL [{ACl II/es 81 5.16 Cen:nkov light scen ln a source scan wtth the semtilla/ors eovered 82 5.17 Attenuation lengths of EMC WLS . . . 83
List of Tables
1.1 Paramders of the liERA collider . , ......... 4
2.1 ComposltlOT! of a Samphng Layer in EMC and HAC. 26 2.2 SU1/lmary of the dl11unslOns of FeAL modules .... 2ï 2.3 Summary of thc dmUIlSlOns of ReAL modules 27 3.1 Radzation Dose from a 2 mGz 60Co .source vs distance. 42 6.1 Summary of Faults in FCAL . 86 6.2 Summary of Fau/ts ln RCAL . 87
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VllI
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:\CI\NOWLEDGEMENTS IX
My work would not be possible without tht:' cOlltributioll" by tl\(' IIH'mlwr" nf tht>
ZEUS collaboration \\ho dcslgned. huilt and preparcd tht' ZEt1S ,'\IUIIII\t'tf'1 1 wlllllt!
likc to thank t}Wn1 for allowing n1(' to pal ti"lpak III ..,\tch (\ WOI t hwhilt· pJl)jt'ct. 1 woultl
also like to thank my sllpervisar David Hanna for al! th(' ad\'ICt' ,md Illotivatiull \-\"Ieh
he provided.
Life in Germany would not ha\'(' bccIl tll(' salllc' Wlt hout t hl' suppurt of th,· fl'I
low CanadJan students, post-docs and profc",solS WOI hing at DES)' who "'t'If' .t1w<lys
willing to help or offer ad vice. AmuIIg them, 1 woult! Mt' to part icularly t ballk J),tVl'
Gill\inson who clic! Illllcb of t}J(' bllildlng alld p\'()grilllllllillg of III<' "0111'('(' dli\t'I, mu:..t
of the insldc :-,canning and, pel h,tpS 1110r(' Îll1pOI tant Iy. illt lodll< <'d 111(' tn IIIp;ht hf(· in
lIamburg.
1 would like to gi\'c very specIal thanks \II\" Gt'!llIan coll('agm'''' CI'nit Cloth. Bodo
Krebs and Focko ~l('ycr, who COI1C.t ructf'd t h(' outsidC' ,,( é-llllwr .\Ild "1)('111 wit Il Ille /1 ltl Il)'
long ddyS and mghts t>canning t\)e modules C('rllt an 1 Fue ho "!lOw(·d /Il(' hu\\" !o 11<;('
their analysib programs as weil pro\ Ide<! me wlth tl)(' \VLS and ''l'ill! illettor attl'llll,tllOIJ
data. Bodo, who led our }ittle group, did llluch of the \ i~\)a! ,lIlaly"!''' of tllC' '>Olll'c('
plots, drew the source driver diagrams and offered IIIally hl'lpf1\1 i>lIggestions.
And 1 must thank my friends and fami!y for their cont in1\al sllpport thlollghollt
this entire endea\"our.
_ ..
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Ch.apter 1
Introduction
1.1 Background
Inquiring minds ha\ (' orteIl posed the questions; Who are we'? and What are we
made of? While phdosophers are still tackling the former, modern science has made
considerable plOglcss towards answering the latter, at l('ast 111 a malerial senSè, during
tll(' pa~t ct'nlury and a halL 5tarting with Mendeleev, who a little over a hundred
j'l'ars ago 01 ganized the PNiodic table, our insight into the underlying structure of
Nat me has grùwn increasingly sophisticated In his time dtoms were J<,lieved to
he the ~lllal1('~t nnits of matter. By 1932 the discO\enes of the electron, proton
and neut IOn :"('l'med to fully explain the structure of the periodic table and it was
thought that they ' ... ere the basic constituents of all things. However, later experiments
using cosmÎc rays and accekrators revealed a ri ch spectruffi of hadronic partic1es,
implying the existence of a great variety of fundamental particles. In 1964 Gell
Manil and Zweig proposed that the multiplicity of hadrons could be explained by
5U(3) S)'11l1l1<'tlY through the introduction of even more elernentary particles call~d
quarks[l]. Today we believe that ail matter is built from six quarks, six leptons and
thC'il' antipal t Ides. They interaet through the intel change of gauge bosons associated
with four fUlldamclltal forces, strong, weak, eledromagneti( and gravitational, which
themselvt's may be manifestations of a single unified force. Already the wcak and
1
CHAPTER 1. INTRODUCTIO.'l .)
elcctlOmagnetic forces are known to be asp{'cts of a single ('lt-ct ro-wl'ak forcI'. .\ Il
paIl ides and threc forces (gravitation excluded) art' acco\llllt'd for by the C\lllt'Ilt l~'
held theOlY callf'd the ·~tanoard model', ~'he glo\\'th uf Olll lllldn ... t'llldllig flUIll thl'
of experiments stlInulating or coufillning, theoretical ideas whit h III tmll forllH'c! tIlt'
bases for further cxpCrimE'llts,
One type of stlch cxperimeuts which has llliHlf' Ill1poltant contllh\ltinll" to tIlt'
de\'eloprnent of the standard rnodel, and in pttrtlCttlar to t he urHkr~talldlllg of 1 lu'
structure of the 111ld('on, is the scattcriltg of leptons by hadlOll" Sill({' ll'ptoll'" tll('
consickrcd to be point particles, they art' ideal for prohing UI\' su b..,t 1 IH t \lit' of t hl' 1111-
cleon. Evidence for the existence of poiutlike, charged 'pal tons' wltr.ill tlle proton Wd.S
first provided in 19G8 at SLAC where cl('ctrons of ('!lf'rgit's 9-16 Ce\' \V1'ft' sca.1t('I<'<! off
protons[2]. Tberc, the s, "th'ring CIOSS sect ions at Ilig'l mOIJWI1! \lm 1,1 tllI"fl"'" l}('h,I\'('d
more like the t'lastic scattering off point-like obj('(ts tlltlll lih(' the ilW],1stl< h!('dhllp
of the proton, Thcse pctrtons were c\'cntually idcntifieJ with tilt' 'lll.llk., pn'violhly
pO'itulated by Gcll-:\taon and Zweig to cxplalO the hadronic Sp<,ctllllll. lIadl Ull'> al'('
belie\'ed to be made of two or three vcl.lence quarks in il ~Cd. of \'11 tuaI quark-c\llt i'lUIU k
pairs. The quarks carry a colour charge and interact maillly tlllollgh th/' .,trollg fo!('('
mediated by the exchange of gl lions in analogy to the e!cd rOlll,lg!wt,ic fOI Ct' W Iw\('
the photon is the mcdiator.
The HErtA accelcrator (sec FigUl~ 1.1) at DESY in ILul1burg will colltd(' :W G('V
electrons with 820 Ge V protons yi('lding a centre of ma:',!> ((Jl\~) ('Ile! gy of v-;, -.: :H 1
GeV[3). As the world's first electron-proton collider, lt. will CO\'('f a rang!' of IIlO/lWn·
tum transfers (Q) reaching up to Q2 '" 105(GcV/c)2, a gn'iü 11I('[(',t,>e fl'Illn pr('\'ioll:',
experiments using fixcd targets which could only f('ach Q2 of il. few hlllld! ('(1 (nt v / r)2,
However the inteJaction cross section dccrcascs roughly as 1/Q1, rllakillg bigh Illmi
nosity a priority in order to acquire sufficient statJstics in the high Q2 1 egion. II EllA
therefore has 210 bunches of both electrons and proton') ('aeh con!.1111 i Iig 0(10 11 ) par
ticles. With a bunch crossing occurring every 96 ns, a luminosity (,( 1 ri' l03i CT/t-2 / S
CIl APTER 1. INTRODUCTION
\
\. ,.,.;~ v . • • \. / .... ~....)f/ ...
\ ..........
HER"
•••••
Figure 1.1: Layout of the HERA Ring
3
can he obtained (see Table 1.1). The distance scale orthe interactions hetween leptons
and quarks which is accessible by HERA is of the order 1O-18cm.
1.2 Kinematics
The principle processes in deep inelastic scattering at HERA energies occur through
neutral current (Ne) interactions exchanging a "( or ZO boson with a parton from the
proton, and charged current (CC) interactions exchanging a W:I: (see Figure 1.2). In
CC processes, the final state lepton is a neutrino and leaves the detector undetected.
In both cases the scattered parton is seen in the detector as a 'jet' of hadronic par
tic1cs emitted in a narrow cone balancing the lepton in transverse momentum. The
remnants of the proton continue on and most are 105t down the beam pipe.
There are only two independent variables in the overall event kinematics, both
of which can be measured Crom either the electron or jet (using the Jacquet-Blondel
CHAPTER 1. INTRODUCTION 4
proton eJectron Parameter ring ring units Nominal energy 820 30 GeV c.m. energy 314 GeV Q~QZ 98400 (GeV/c)1. Luminosity 1.5.1031 cm-1.,,-l
Number of interaction points 4 Crossing angle 0 mrad Circumference 6336 m Magnetic field 4.65 0.165 T Energy Range 300-820 10-33 GeV Injection energj 40 14 GeV Circulating currents 160 58 mA Total number of particles 2.1 . 1013 0.8.1013
Number of bunches 200 N umber of buckets 220 Time between crossings 96 n" Total RF power 1 13.2 MW Filling time 20 15 min.
Table 1.1: Para met ers of the HERA collider
e
e
y.z·
p p
q'
Figure 1.2: Feynman diagrams of lowest ortler a) NC and b) CC interactions .....
( ...
CHAPTER 1. INTRODUCTION 5
mcthod[4]) alone. 1'0 define the kincmatic relations we let Pe and PI be the four vectors
of the incollling and scattered lepton respect1\'ely, P that of the incoming proton, and
Cf = pf' - PI that of the exchange boson.
Tite total invariant mass squared is
The approximation assumes the particle masses to be zero, which is very reasonable
at lIERA energies. The square of the four momentum transfer, QZ, is defined to be
positive
Q2 - _q2
:::: -(Pe - PI)2
~ 4E E . 2 (JI e 1 sm 2'
The encrgy of the CUITent in the target rest frame, Il is
Il == p.q
mp
2Ep 201 ~ -(Ee - Eicos -).
nlp 2
The dimensionless variables Bjorken-x and y are given by
Q2
2P·q x =
y
Q2
2mpll
EeE, sin2 ~ ~
Ep(Ee - El cos2 ~)
-
=
::::
~
p.q p. Pe 2P 'q
S Il
IIma:r
Ee - EICOS2 ~
Ee
CHAPTER 1. INTRODUCTION fi
They are always in the range 0 $ (x,y) ~ 1. In the parton model, x can be identified
with the momentum fraction of the proton carried by the struck parton wllC'reag y
is a measure of the inelasticity of the event. A nothC'r uscful quant ity, the invariant
mass ~V of the hadronic system, is given by
w2 = (q + p)2
2 1 - x 2 = Q --+mp.
x
An accurate measurement of the kincmatics of an event requires a high n'solut iOIl
hermctic calorirneter. III the case of CC proccsscs, one cannot \11eaSl\I'e tht" o\ltgoillg
lepton and must instcad rely on only the jet meaS\lrCllwIIts for a dt'sn ipt ion of t.he
event. Even ",hen the clectron is present, as in Ne proceS~l'S, t.he ('If'ctron is oftf'n in a
kinematic reg,ion where a small error in the measure'ment of the t'le( tWIl'S /llOIlH'lltlllll
means a large error in x or Q2 (see Figure 1.3), Although traching detf'ctor~ aIso
give momentum information, their fractional resolution, <7p /p, grows linearly with
p. In addition, they are effective only for chargcd particle~. On the othel hanrl, a
calorimeter has a fractional resolution improving as liVE and is sensitive to same
neutral particles as well as charged ones. Using the calorimctf'r for Ilwasuring the
event kinematics also requires it to have fine segmentation for good angular n'solution
and good hadron-electron discrimination to distinguish electrons flOm pions.
1.3 HERA Physics
A broad range of physics prospects is available at HERA [5]. Structure functians,
h{~avy quark physics, compositeness, low-x physics and searches for exotic particles
such as leptoquarks are aH potcntial of areas of rescarch. III particular, the study of
the evolution of the structure functions of the proton with Q2 is of prime importance.
These structure functions, whià dcpend on the probing leptons' polarization, arc
related to the quark and gluon densities of the proton. The cro"" ""ri ion (or dcep
.'
l
("
GHAPTER 1. INTRODUCTION 7
FINAL LEPTON S 4
CURRENT JET 100 GcV t- of
Figure 1.3: Polar diagram of the kinematics for the jina/lepton (upper part) and the
current jet (lower part) with lines of constant x and Q2. Connecting a given (x, Q2)
pOint with the origm gives the laboratory momentum vectors, as shown 611 the example
for x = 0.5, Q2 = 50(lOGeV2•
CHAPTER 1. INTRODUCTION 8
inelastic scat tering is expressed in terms of the structure functions Ft, /<'2 and F3 by
ducing secondary eledrons and exeÎted atoms. The pnprgy los ... pel' unit lt'lIgt.h
go cs as Z log Z.
From Figures 2.1 and 2.2 we can see that an EM sl1o\\'CI' will go through twü
stages. In the beginning energetic pal'ticles 108e cIlelgy thro\lgh br('msstrahhmg aud
pair production. This continues until the pal tide rcadws a (,PI Utin thrp"hold CIWlgy,
called the critical energy €c, at which the energy loss to brems~j rahlllTlg ih ('qu,t! 1.0
the ionization Joss. Afterwards, in the later stage of the S}lo\\W, "ItOW!'1 parti!]P~ Jo,,('
their energy through ionization bdorc bcing able tü producc ncw pal ticlcf, dnl! hhower
mu1tiplicatioll stops. This ionization energy dcpo!:>ited by lo\\' cnergy paIl icl('~ al, 1 be
end of the shower constitutes a large fraction of the measUIcd signal. Th(· CI il.Î( al
(
(
CHAPTER 2. THE CALORIMETER
-• -. , .. ..J
"'1-'0'0
-114.1 ,
E (MeV)
020
Ol~
{ u
010 ~ c ::1
OO~
1000
17
Figure 2.1: Fractional Energy Loss for Electrons and Positrons in Lead (from Rev. of
Part. Prop., Phys Let. B. Vol 299)
••• '.H
• •.• l '.14
'.'2
Figure 2.2: Photon cross-section in lead as a function of photon energy. (from Rev.
of Part. Prop. 1980 edition)
-
CHAPTER 2. THE CALORIMETER 18
energy le can be parametrized by [10]
f c :::= 800 [ AI e V]. Z + 1.2
We describe the longitudinal and transverse devclopmcnt of a showpr in terms of
radiat,ion lenGth and of Molière radius. The radiation length, Xo, of a mat<'rial is tlH.'
distance a high cnergy electron must travel for its energy to drop to 1 je of its original
energy purely due to bremsstrahlung. It can be approximated hy [11]
The average distance a very high energy photon trave1s before splitting into an e+ e
pair is 9/7 Xo. The Molière radius, R.u, is a measure of the radial devdopnwnt of
an EM shower. Most of the contribution to the radial spread cornes From multiple
scattering of the electrons. 95% of the total energy of a shower is contained in a
cylinder of radius approximately 2 RAI. It is roughly givcn by
For a DU-scintillator calorimeter, the Molière radius is about 2 cm.
The average amount of energy deposited at a given depth from the face of a
calorimeter by EM showers can be parameterized according to [121
dE ba+1
E a -bz dz = r(a + 1) z e .
Here the constants a and b have a logarithmic dependence on energy :
a = ao + al ln E
b = bo + b1 ln E,
where for the ZEUS calorimeter the values are: ao = 1.1,5, al = 0.54, ho = 0.395/ X o,
bl = 0.022/ X01 E is in GeV and Xo is in cm [13]. Longitudinal shower profiles are
shown in Figure 2.3 for electrons of energy l, 20 and 75 CeV.
{
CHAPTER 2. THE CALORIMETER
J r 0" .. t 0'.
012
0'
001
001
oa.
002
°0
1
1
. .. . ..
1
1
1
.. 1
'. ............ ........ \1 20
19
21
Figure 2.3: Average deposited energy vs depth for electromagnetic showers of energies
l, ~O and 75 GeV
2.1.3 Sampling fraction
The sampling fraction, defined as the fraction of a particle's energy deposited in the
active layers, plays an important role in determining a calorimeter's resolution. This
sampling fraction, R, of a particle is given by
R - Evu - , E"j, + E,Av ••
where Ev;. is the energy deposited in the active layersj Etrun.. is the ellergy deposited in
the passive layers. The different types of particles produced in a sbower have different
sampling fractions. For electrons and hadrons we denote the sampling fraction by e
and h respectively. Sampling fractions are uS'lally compared to those of minimum
ionizing partides (mip). These ficticious particles have a sampling fraction given by
wbere i runs over ail tbe different media; tl is the thickness of a layer of medium Îj
dEddz is the minimum energy loss per unit length in medium i, and act is the active
medium. Muons have a sampling fraction close to a mip and are often used as mips.
CHAPTER 2. THE CALORIMETER 20
For an electron the cjnllp ratio is less than one. The rt'é\son is due ta the dif
ferent Z dcpendence of the cross sections of the various intclactiol1s oCl'urril1g in an
electromagnetic sho\\'er. ln the course of an e}ectl'omagnctÎc show('r m,Hl!, low t'Ill'rgy
gammas are produced. For these photons the photo<'lcctri<: df<,ct, is the dominant.
interaction. Since the cross section of the photoclectric e{fcct gacs a.s Z5, t IH'y are
predominately absorbed in the high Z absorber rcgion. The resulting 10w elll'rgy
electrons have a very short range and mO!,t do not rearh the scintillator. The e/mip
ratio for a DU jscintillator calorimeter is about .62 and is ollly slightly depende/lt on
energy.
2.1.4 Hadronic Showers
Hadronic showers are created through the inelastic scattcring of the strongly int.eract
ing hadrons and their sccondary particles by the nuclei of absorber llHÜ<'l'ial. A wide
variety of different particles are produced, with differing energy 10ss '_H'chanislns. A
summary of the particles found in the cascade is provided below.
• Charged hadrons such as ]('s, 7I"'S, and p's which lose energy through ionization.
• 1/"°'S and ",'s produced from the decay of hadronic resonances. They d('cay into
two ')"s and deposit their energy in the fonn of electromagnetic showers.
• High energy neutrons produced in the intranuclear cascade during spallation.
• Low energy neutrons released through evaporation of excitcd nuclci.
• Low energy gammas produced in fission processes and thermal neutron capture.
• Neutrinos from particle decay.
We can define a nuclear intera,·tion length, À in a similar manner to to the radiation
length. >. is the average distance a hadron travels before colliding with a nucleus:
(
c
CHAPTER 2. THE CALORIMETER 21
where NA is Avogadro's numbcr; A is the atomic weight of the nucleus, and O'abJ' the
nuclcar ab~orption cross section, is proportion al to A711 [14).
Then the average longitudinal profile of the energy deposition in hadronic showers
can be wriUp!l as
where a and b have the same values as in EM showers[15J. For a model of the ZEUS
calorimeter a = 0.16, 9 = g1 + g21n E, g1 = 2.86/ À and g2 = -0.50/ À and À = 23.6
cm.
The transverse dimension of a hadronic shower grows logarithrnically with the
cnergy of t.he shower. The width, W, needed to contain 99% of a shower in an iron
Iiquid argon calorimctcr Îs [16]
W(E) = -17.3 + 14.31n E [cm].
The particle diversity causes the rcsolution to be worse thall pure electromagnetic
showers. Each type of particle has its own sampling fraction. Neutrinos and sorne
of the neutrons will totally escape the calorimeter without being detected. AIso,
the energy loss in breaking up the nuclei is not seen. Heavy charged particles will
dcposit cnergy through ionization si!TIilar to a mip. The lI'°'S and the 1]'S have only a
fraction of a mip's signal. The fluctuations of the proportions of particle types and
the intrinsic fluctuations of hadronic showers are the main contributors to the energy
resolution ~f hadronic calorimeters. The extra undetected energy losses cause el h to
be usually greater than 1.
A large source of fluctuations in a hadronic shower is the fraction lem which is
in the form of an electromagnetk shower. This fraction can vary widely from event
to event with the production of high energy 1I'°'S and 1]'S early in the cascade. If the
response from the electromagnetic and hadronic components of a shower are not the
same, the resolution of the calorimeter to hadronic showers will be seriously degraded.
Moreover, f~m is energy dependent and non-Gaussian.
..
CHAPTER 2. THE CALORIMETER 22
2.1.5 Compensation
Due to the presence or the electromagneti-.:ally decaying 1r°'S and 1] 's, hadronic showcrs
have both an EM component and a nonelectromagnetic component. If tlH' elh r:itio
is not l, the non-Gaussian fluctuations in Itm will cause CTZ,J "7 ta Ilot impro\'c:' as
liVE. At high energies the resolution will approach a llonzero constant tt'I'm. ln
addition, the tnergy dependence of lem causes el h to be 3180 cnergy dt'jwndent ThIs
lesults in an alinearity in the calorimcter signal which cO\llcl bias tI iggers La.::;ed 011
enelgy because the detected energy of a single encrgeti(' partide wOllld he cliff('n'Ilt
than that of a jet with the same total energy. 19noring dctcdor imp(" [ections, tht'
resolution of a hadronic calorimeter can gcnerally be writt('ll as
~ = A/tabll + B(ejh - 1) E JE '
where tabs is the absorber layer thickness, A = (T2 mtr + (T2 Mmp) t is tllP contri bu
tian from intrinsic fluctuations, nuclear binding losses and sampling fluet uat.ions and
B(O) == o. In order to achieve ej h == 1 we have to compensate for undetected energy losses
due prirnarily to the breaking up nuclei. We can either suppress the calorirnetcl"~
response to the electromagnetic component of the shower or incrcasc the respOllS<'
to the hadronic component. Most of the compensation is usua l1y attélJned through
augmenting the hadronic response. For example the use of deplcted uranium platc!>
increases the hadronic response due to the extra en~rgy released during fission pro
cesses. However, the most significant factor in increasing the hadronic rcsponse is
the a.mount of energy neutrons transfer to a hydrogenous medium. It hll'ns out that
in the final stages of a shower's development most of the showcr's energy is sp('nt on
nuclear processes. Low energy neutrons, protons and gammas arc produccd. Many
more neutrons than protons are released, especially in large Z matcrials. Thes/' soft
neutrons are eventually recaptured and lose their energy invisibly through e1a:,tic
scattering. However, if the calorimeter contains hydrogen in the readout matcrial,
much of this lost energy will be l'ecovered. The neutrons can transfer a large propor-
(
Cl/APTER 2. THE CALORIMETER 23
tion of their kinetic cnergy to hydrogen, prorlucing recoil protons. These low encrgy
(l'V 1 MeV) protons have a very short range and becausc they originate in the active
meltcrial, they are Ilot sam pIed. Instead, they will deposit ail their energy in the ac
tive calorimeter layers. However, saturation of the medium can limit the extra light
contribution from the ionizing protons. This is parametnzed by Birks law,
dL == A dEldx [cm2 j g). dx 1 + kBdEjdx
where L is the light yieldj A is the absolute scintillation efficiencYj kB Îs a parameter
relating the dCl1'3ity of ionization centers to dEI dx. Ncvertheless, the net result is a
decrease in the el h ratio. The amount of compensation can be chosen by varying the
relative thicknesses of the active and passive layers of the calorimeter, or by adjusting
the fraction of hydrogcn atoms in the sampling medium. A final adjustment can
be done by changing the signal integration time which determines what fraction of
delaycd gammas from neutron capture contribute to the signal. The elh ratio can
also be reduced by lowering e. This is done by inserting a low Z foil between the
active and passive laycrs. This prevents photoelectrons produced at the boundary of
the high Z material from reaching the a,ctive layers.
Compensation has been achieved for uraniumfscintillatoI and lead/scintillator
sampling cc:tlorimeters. In order to be compensating, a DU/scintiHator calorime
ter must have a scintillator/uranium volume ratio of about 0.82. The volume ratio
is about 0.25 for a scintillator/lead calorimeter. This means that a compensating
leadjscintillator calorimeter of the traditionallayer type sampling variety would Juf
fer from larger sampling errors than the DU Iscintillator \'ariety if normal scintillator
thicknesses were used. Partial compensation has been achieved using liquid argon.
In this case neutrons transf~r their energy tü argon in the same way they do with
hydrogen, but with mu ch less efficiency. At most only 10% of the neutron's energy is
given to the recoil argon atom and this also occurs with a lOWf'f rrn'lS section[8]. It is
also possible to improve the rcsolution of noncompensating calollllld ('rs by estimat
ing the fraction of energy deposited through 11"0 deray and then appIj illg weighting
algorlthms. This would require a fine longitudinal separation in the readout and was
CIIAPTER 2. THE CALORIMETER 24
fil'st attempted by the CDHS expel'iment[lï].
The hadronic t'nergy resolution of a compensating DU j~ciJlt illatol' calorillwtel' is
thc quadratic sum of its illtrmsic and sampling l'csolution :
a(E) 22% 0.09J~E(1 + l/Npe ) -- = --ffi --E JE vIE '
where E is in GeV, ~E is the energy loss pel' layer in l\1eV and Npe is the numbel' of
photo-electrons seen in the phototubc. This yiclds an energ}' r('solution fol' a typical
calorimeter of a(E)jE = (33% - 35%)jJE.
2.2 The ZEUS Calorimeter
Motivated by the need for a high resolution calorimder to satisfy the physirs 1'('
quirements, the ZEUS collaboration began u.'dertaking in 1985 d('sign studies for
a depleted uranium - scintillator calorimeter. Only after an extensive plOg,ratn with
test calorimeters and Monte Carlo studies was the design fin \lizcd [18). The sa III pli ng
thickness in the EMC and HAC section was chosen to be 1 .xl. leading ta a DU plate
thickness of 3.3 mm.
The DU plates are fully encapsulated by a stainlcss steel foil of 0.2 mm thickn ... ss
in the EMC and 0.4 mm in the HAC. The steel foil a11owe(1 saCe handling of tlw DU
plates during construction (the main concern was uranium dust), as well as a reduction
of the signal contributed by the DU natural radioactivity. This radioactive signal
(UNO) has to be low to minimize noise and radiation damage to the scintillators but
large enough to be used for intertower calibration. The choicc in DU plate thickm'ss
required a scintiUator layer thickness of 2.6 mm to achieve efh = 1.
The scintillator used is SCSN-38. It has a high light yield, low light attenuation
and good stability against aging and radiation. The use of plastic scintillator with its
fast decay time of the order of a few nanoseconds allows a very good timing rcsolution.
This is important in reducing the background from cosmic ray and bcam gas evcnts.
The fast response also alleviates pileup problems arising from the short interbullch
(
CJJAPTER 2. TJ1E CALORIMETER 25
crossing time. The composition and properties of the sampling layers are presented
in Table 2.1.
The EMC sectior. is made of 25 DU /scintillator layers. It is followed by the HACI
section and ,in FCAL and BCAL only, the HAC2 section, each with up to 80 layers.
Aside from the 60Go sources, the calorimeter uses two other calibration systems. The
UNO mC/ltioned above allows the normalization of the signal from towt'r to tower
without having to subject every tower to a test beam. Test results have shown that
e/UNO (the ratio betwcen an electron's signal at a given energy and the UNO signal)
betwf'cn diffcrcnt calorimcter towers is constant to wit hin 1.1 % in FCAL and 1.5%
in RCAL[19]. The other calibration system uses pulsed laser light fed to the base of
the light guide by optical fibres to monitor the linearity and long term stability of the
photomultiplier tubes.
The calorimeter subcomponents are divided into modules. BCAL is made from
32 identical modules. FCAL and ReAL each contain 24 modules, two of which are
half and positioned above and below the beam pipe. A summary of the dimensions
of the modules in FCAL and ReAL is given in Tables 2.2 and 2.3.
Each FCAL/ReAL module il; 20 cm wide and has a height varying from 2.2 to
4.6 m depending on it:; pOE: ".l11 to the beam. Thus the number of towers in a module
ranges from Il to 23. Figures 2.4 and 2.5 shows the positioning of the FeAL and
ReAL modules.
2.3 FCAL/RCAL Modules
The modules for FeAL and ReAL were assembled by the Netherlands and Canada
[19][20][21]. Each consists mainly of a stack of depleted uranium plates and scintillator
tiles supported by a steel C-frame (see Figure 2.6). The C-frame has three parts, the
end beam and the upper and lower C-arms. The end beam supports the stack of
scintillator and DU plates during assembly and transport. Running along the end
beam are two trays housing the optical fibre bundles for the laser system and the
CHAPTER 2. THE CALORIMETER 26
material thickness thickness thickness [mmJ [.\oJ [ÀJ
EMC steel 0.2 0.011 0.00i2 DU 3.3 1.000 0.0305 sted 0.2 0.011 0.0012 paper 0.2 scintillator 2.6 0.006 0.0033 paper 0.2 contingency 0.9 sum 7.6 1.028 0.0302 effective .\"0 0.74 cm effective À 21.0 cm effective RAI 2.02 cm effective (e 10.6 ~leV effective p 8.7 gjcm3
HAC steel 0.4 0.023 0.0024 DU 3.3 1.000 0.0305 steel 0.4 0.023 0.0024 paper 0.2 scintillator 2.6 0.006 0.0033 paper 0.2 contingency 0.9 sum 1 8.0 1.052 0.0386 effective Xo 0.76 cm effective À 20.7 cm effective RM 2.00 cm effective (e 12.3 MeV effective p 8.7 gjcm3
Table 2.1: Composition of a Sarnpling Layer in EMC and lIAC
4 Meter 3.10 Meter . . . .... ...... --... ! 1 ,/ "'" 1
i ll: I~, ... j ........... ou ••• ("' :~:;d-t;~:.~·· .... ····· t .::::::: lE' ..
.. 100 mm
•• , ,
,lo.... ~ ,/ -------....-
-3mm steel .eal
•
,
l ~l.œ~-R~-~r~r-~\ii paano ) ~! L- ___ ,
Figure 3.5: Source wire used in outside scanning
CHAPTER 3. 6(JCO SOURCE SCANNING 53
~_M_A_G_T_A_P_E __ ~I~~ ____ D_IS_K ____ ~ .r-~
DISK MUX-ADC
INTEGRATORS
HV CONTROLLER
PM TUBES
DECODER DRIVER
{ Figure 3.6: Layout of Elements in the Run Control
CHAPTER 3. MCO SOURCE SCANNING
1
.otor
. ....... ,-.
base plate
Figure 3.7: View 01 Source Driver Irom above
dial 8Otor
Figure 3.8: View 01 Source Driver Irom the side
(
Chapter 4
Monte Carlo
Il is often helpful in understanding complex systems to simulate them \Vith Monte
Carlo programs. The adual processes involved may be individually relatively simple,
but multiple consecutive interactions can quickly hecome exceedingly complicated
and not analytically solvable. In our situation, the process of shower development
is statistical in nature and lends itself naturally to Monte Carlo studies. The Monte
Carlo program EGS4[28] was used to simulate the 6OCo scans. It is a successful
program for simulating elcctl'omagnetic showers.
The user has only to define the detector's geometry and properties of its materials,
specify the initial conditions of the input particle, choose the energy cutoffs and
kc<,p t.mck of the cnergy deposition. Every region has an energy cutoff ECUT for
e!('clrons p .u peUT for photons under which they will no longer he tracked. The
particles are then assumed to deposit aIl their energy in that region. EGS4 (or its
preprocessor PEGS) calculates the interaction cross sections for the rnaterials. The
user defines rnaterials as compounds or mixtures of elements. For every material an
AE and AP must be defined. AE and AP are respectively the energy cutoffs for
electron and photon production in the material. Particles move in small steps, with
each step bringillg them either to an edge of a region or to the point of their next
interaction. Also, for low energy electrons, a step size, which is the fraction of an
electron's energy lost to ionization per step, can be set.. This gl"nerally decreases
55
. '
CHAPTER 4. MO.'\'TE CARLO
the step di~tallc(, for low energy clectrons, increasing the accllracy of their tracks .
~atUl'ally the accuracy of the simulation improvcs with the low('ring of the PIl<'rgy
cuts. CnfOltunately the computation tinw incr<'1\ses as wl'II SI'\('lal ditfl'I(,l\t cuts
were tried out and t!lC!C did not Scem more than a fl'\\ Pl'ICt'lIt difTl'I('IIC<' !}('tW('('1l
them. However the computation time varied sigllificantly. The COlllputdtion till\('
was Ilot significantly lcngthcned by using the lowest 'Berg)' cut allo\\'('d for photons;
10 keV. Belo\\ this limit the approximations for the cross sectIons blt>éÜ. <lo\\'n. The
main drain of CPU time are the electrons, which maye in small steps, depositing
ionization energy and un(l ergoing multiple scattering Th{' au! bon; of tilt:' plOgram
rccommend using a smaller than default stcp size when dCilling wlt.h thin la)f'l's. ln
the end nonstandard cntoffs were used: FeUT ::: 1.0 Me\', }l('\1'}' = .0\ ~I{'V, AE
= .711 ~lcV and AP :.::: 01 ~1eV everywhere. A step size of 5% was used for sU't'l and
scintillator. The default step size wa:; used in uranium, SlIll'(' it was a~~l\IJ1{'d t hat
most low energy clec! rons would Ilot escape the mélIlillIll ond »<'1]('1,1 ctte t hl'ough the
steel foil surrounding it. For a million ('vents it took about .1 Itol\rs ('Pl! on a VAX
8600.
In the l'l'al 60Go scans the data is takcn rollghly every .5 mm in the longitudinal
direction, z. If we were to simulate the GoGo scans in the same mannf>r, i.e. by
repositioning the source longitudiually along a tower, the étlllOlint of computer lime
required would be prohibitive. Instead, we can take advantagc· of the p .. riodicity of
the layer structure of a BAC section to find the signal re"'ponsf', R(z), of a singlp
scintillator as a function of the source distance in the longitudillal directioll from the
centre of the scintillator. We can then convolutc the respon,>e fI 0111 a ~illgl(' ~(intillator
to get the signal from an entire section. A way ta do thls is la fil~t deflll<' tl)/' g(,olll('try
as having a lalge stack of DUjscintillator (in this cast"' 120 Id)els) to avoir! havlIlg to
worry about edges. The number of layers is not irnpol tant a~ IOllg o.'> t}l(> dl~tallce
from the middle to the end is greater tItan the range of ;; III whi< h Wt:' éIlC int('r('~t('d.
Next wc run the Monte Carlo with the SOUfC(' along the stack al 8 dlfTf'f<'nt po~itions,
spaced 0.5 mm apart in the z direction, starting at 0.2.5 mm f/Olll the (f'utn' of the
( ..
CHAPTER 4. MONTE CARLO 57
middle sc:intillator (callcd the Oth layer, but actually the 60th of the 120 layers) of
the !>ta.ck lü .1 Î!') Illlll from the centre. At the eighth position the source is actnally
oppo.,it(· an III iiniulIl layel If the "ource is at a distance z from the middle of the Oth
layer, thcn il i~ a di~t,U1ce 8z - z from the middle of zth layer. This means that for a
source ::.itting at position z, the energy deposited in the 7th scintillator is R(8i - z).
If wc also use the fact that R(z) =- R( -z) then the Oth scintillator gives data for 0.2.5
- 3.7.5 mm; the 1 st scintillator covers 7.75 mm to 4.25 mm; the -lst scintillator is in
the range 8 25 mm to Il.7,) mm and so on. By combining the information frorn each
scintillator layer we can construct R(z) for any z. This function R(z) obtained does
have a slight correlation between points separated by a multiple of 4 mm because the
values were gcnerated by the same Monte Carlo fun, but it should be removable by
smoothing algorithms.
Once we have R(:) wc can find S( z), the SUffi of the l'esponses of eighty layers, by 79
S(z) = Ec,R(z - 8l),
whcre CI i., a measure of the efficiency of scintillator layer i and z = 0 mm is the
location of the Oth fcintillator.
A simplified but nevertheless detailed geometry of a HAC section was used. This
is shown in l'igure 4.1.
The tower was assumed ta be large stack of DU fscintillator tiles. The 60Co source
\Vas treated as a point source emitting 1.17 and 1.33 MeV photons with equal prob
abitity in a random direction in the hemisphere towards the tower stack. The source
was placcd outside the module as in an outside scan and 5 cm away in the laterai
direction From the centre of the tower.
The raw shape of the source response is shown in Figure 4.2. The error bars ar~
purely statistical and have no bearing on how weIl this shape matches the l'cal results.
Actually, special measurements \Vere done on severai towers with the 60CO source.
ln one su rh measurement, the strap was removed and the edges of al! but one sein
tillatol' layer wcre co\'ered. A 60Co scan was then done normally. Figure 4.3 shows
the l'cal response of a single scintillator. The fundion obtained from th~ Monte Carlo
CHAPTER 4. MONTE CARLO 58
1
)59 more 1 l 1 1 1 1 1
loyers 1 200 -0.65
AIR
2.6 SCINTILLATOR 0
:o-6C ,-... Cl> sourCE 065 -..... AIR QJ (f) U1
\ 0 0.4 (f) V1 u
FE cr: -l -l + cr ~ ~ 3: < c-
o ~ ..... (f)
'-'" 3.3 URANIUM w w 0:: 1.0 ~ u... <
2.0
0.4 FE 2.0
0.5 z l60 more 0.4 06
3.0
Lx loyers
-
Figure 4.!: Layer Structure used in Monte Carlo Simulation. Distances are in mm.
'600
CHAPTER 4. MONTE CARLO
1
j '200 r
~
~ 800 l
!
le"",,)
t
i \ 1 r r
o
\
\
59
1 . 1
l j ~
, .., . " '~'lij
~o ,~ 100
Figure 4.2: Monte Carlo of the Response function, R( z), of a Single Scintillator,
before and after smoothing
, r · 7 _
, r •
~ -t . ~ ·
3 ':. · ~
1 2 ~
.,~
r 1
,,;
~ ,1 . , ,
\
\ .. \
... '\
~ .00 U~ ,~ t'~ 1000 toa=- 'ose ton
-'-'1-1 "'''''yl. IIIL" ru. 2~~ CODQIt ,ft To •• t 12 [WC, /O'C2l ,... l'lAC'.
Figure 4.3: Real Response of a Single Scintillator
-
CHAPTER 4. MONTE CARLO 60
is slightly nalrower thdn the real response but othel wise reproduct's tlH' !-Ih"lH' [.urly
weIl.
After doing a S poillt filter on the law shape [rom th(' ~!ontl' (';\110 •• \I\t! SlI\I.lut hing , the distribution wilh the HBOOl\ loutine llS~100F Wl' Cdn appl) tht' ,d,u\'t' 'fOrI Il Il 1.\
to get the shape of a 60Co scan from a 'good' BAC ~('ction (s('t' Fig,I1r(> .1. 1) The l'\
point filter averages over the eight neart':,t points. The filt('ring alld Sllloot hlIIg wlllt'h
decreases the correlation between points c;eparated by 8 IllTll also ~igllificalltly ~muot hs
the peaks and valleys rcpresenting scintillator and DU layers after (,o1\vollll iOB. This
plot of the H:\C section and the succecding oneS \\ere ill faet llIade by takillg thn'('
Monte Carlo runs to find the response functions for scintillat.or!'l proj('( ting floll\ t II<'
uranium by 0,0.6 and 1.2 mm. Then in the convolution, 80% of IIIC' !'Icillt.illalols wert'
assumed to be projecting out by the nominal distance of O.G mlll 'l'Il(' rl'lJlailllllg :.?O(,:{,
were assumed to be pu shed in or out by another O.G mm and Il:-.(·<1 t ht' <lpplOl'll"t('
response function. The redl sciutillatoIs are exp('c1('c! .,hghtly :"llIftt·d hl'( <Ill"!' of t II!'
culouts in the scintilldtor for the spacers ale slightly Ictrg,cr t h<lll tilt' "!lM!')' ~JZ('.
This makes the shapcs of the individ ua} scintillatOl peaks ~e{'m les:" 1 <'gllictr éllld mort>
realistic. In addition, we assigned randornly to the coeffici(>llt c, of R, (z) a valllt'
between .95 and 1.05 to reflect minor uncorrelatcd variancc5 in scilltillator thickll('s.,
or WLS uniforrlllty.
We can sirnulate what potential errors would look lik(' by adju!-II ing l'a tü mimic t 11(>
effects the errors would have on the the light output of the sClllttllators. For ('xalllplc,
Figures 4.4 - 4.7 show plots with a 50% shadowed 5cintillator, bad stacking with !-IomC'
scintillators pushed out, bad stacking wilh sorne scintillators pu<;hed in, and a lill('ar
dip in WLS response of 20% in the first 20 laye' s.
With the Monte Carlo we can investigate in detail somc of the factols which affect
the 6flCO scans which cannot be easily discovered expcrimcnt ally. For ('xalllpl(" the'
average depth where energy is deposited in the scintillator and con~cqll('ntly, whcrc
light is produced, is rcvealed through the Monte Carlo to be about }(J mm. Figllre 4.9
shows the deposition of enelgy sumrned over ail the scintillators in the x-y plane wlth
(
c
CHAP'fER 4. MONTE CARLO
~ ii > ; 1. 0
P '" Jo 0 r
11000
7000
6000
5000
JOOO
1
1
1
::~ o 0 'OO:-~2=00~-~J~00~~.00~--~~00·~--~600~--7~00~~
No, mOl ti&C Sect1ot'l Sourte t)OlltlO~ lmm)
Figure 4.4: Convoluted Response Fundion Representing Signal From BAC
i ~ l. 0
l 0 r
11000
7000
6000
!IOOO
4000
JOOO
2000
1000
thodo •• d ICInt
100 200 .00 100 Soure. _,\_ (mm)
Figure 4.5: Atonte Carlo HAC section with one scintillator 50% shadowed
61
1
t
CHAPTER 4. MONTE CARLO 62 . ! ---_ .... -- -. ,
9'lQ() i 1 , "t'd"CeG '*lS '."0 &
1~Jr(r~Itf~I(fIIIfhM~ Z; !OOQ : 5 , " 1 <
'" 'aoe : ;, e • Il. ,
J , 6COC ;
, ,
5000 l , \
1 '000 t
1 1 ,
lOOO r 1
2000 t 1000 r
o ~---- ~--~-"" o 100 20C Joo '00 '>00 600 100 800
ShOl"tldt" Soufte POSI\'Of"I (mm)
Figure 4.6: Monte Carlo of HAC sectIOn wlth damaged WL8. The first 20 layfr!> hal'f
a reduction in Z'ght output of 20% for the first laye l', den'easzng lmear/y to 0% for the
tWf.71ty-ji.rst layer.
JOoo
.00 -~- -600-- 700 100 200 100
Figure 4.7: Monte Carlo of HAC section with 120 layers pushed in by .6 mm